Fundamental normality test explained

In complex analysis, a mathematical discipline, the fundamental normality test gives sufficient conditions to test the normality of a family of analytic functions. It is another name for the stronger version of Montel's theorem.

Statement

Let

l{F} be a family of analytic functions defined on a domain \Omega . If there are two fixed complex numbers a and b such that for all ƒ ∈ l{F} and all x ∊ \Omega , f(x) ∉, then l{F} is a normal family on \Omega .

The proof relies on properties of the elliptic modular function and can be found here: Book: J. L. Schiff . Normal Families . Springer-Verlag . 1993 . 0-387-97967-0 .

See also

• Montel's theorem